Pretty much this.
You'll sit in more traffic in the short journey from home to Dover than you will Dover to Nice.
Consider buying a toll tag before you go.
Do not know, the site translated would suggest you can do that but I had a little search online. The TUV is their DVLA I think, they seem to have 2, North and South.
https://www.tuev-nord.de/en/private/traffic/car-motorcycle-caravan/emissions-sticker/order/...
Crit'Air vignettes? Buy direct here: https://www.certificat-air.gouv.fr/
Germany you need to buy from each locale. For Cologne it seems like you need to buy in person but I've never driven there: https://www.stadt-koeln.de/service/produkt/feinstaubplakette-1